Adaptive Estimation of Convex Sets and Convex Polytopes from Noisy Data

Abstract

We estimate convex polytopes and general convex sets in R, d ≥ 2 in the regression framework. We measure the risk of our estimators using a L-type loss function and prove upper bounds on these risks. We show that, in the case of polytopes, these estimators achieve the minimax rate. For polytopes, this minimax rate is lnn n , which differs from the… (More)

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Cite this paper

@inproceedings{Brunel2012AdaptiveEO, title={Adaptive Estimation of Convex Sets and Convex Polytopes from Noisy Data}, author={Victor-Emmanuel Brunel}, year={2012} }